Optimization of Factors of Safety and Displacements of Unsaturated Soil Slopes by the Bioinspired Metaheuristic Method

Abstract

The present work introduces an analytical framework based on the limit-equilibrium method for the determination of the local factor of safety (FS) and global factor of safety (FSG), and local displacements along the critical slip surface using the Morgenstern–Price (MP) method of slices. This proposed work computes displacements along the critical slip surface in addition to a single FSG. The unsaturated shear strength models, in conjunction with the soil–water characteristic curve (SWCC), are considered. The MP-based equilibrium equations to determine FSG are utilized as an objective function in the metaheuristic search algorithm of particle swarm optimization to determine the critical center, critical radius, and minimum FSG for unsaturated finite slopes. It is recommended to use a particle size of 75 and conduct 50 iterations for optimal results. The effects of SWCC fitting parameters on the critical slip surface, FSG, point FS, and point displacements are also investigated. Two distinct benchmark slope scenarios with and without negative pore water considerations are utilized in the current study. This approach enables a detailed investigation into the influence of various unsaturated soil parameters, such as af (related to the air-entry value), nf (related to the slope of the SWCC), and mf (related to the residual water content), as well as constitutive model parameters including the linear shear modulus (G) and the fitting parameter (ρ). The maximum displacement occurs at the slope’s top crest. Under benchmark conditions, the first scenario shows a reduction in point displacement by 3.30%, 1.98%, and 10.23% for SWCC-1, SWCC-2, and SWCC-3, respectively. However, in the second scenario with SWCC-3, the critical slip surface’s position changes, affecting local displacements. This results in an increase of 32.72% (i.e., from 21.45 to 28.47 mm) in point displacement at the top when comparing SWCC-3 with no SWCC consideration. The current study advocates that the effect of fitting parameters of the SWCC should be used to better understand the local FS and displacement, because the critical slip surface is contingent on the values of the SWCC. Ignoring SWCC parameters can lead to an underestimation of slope displacement, because they significantly influence the critical slip surface position and displacement magnitude. Their inclusion is essential for accurately assessing slope stability and preventing errors in displacement prediction. The proposed analytical framework has significant practical applications in geotechnical engineering, particularly for slope stability analysis and design. By computing both global and local factors of safety and predicting local displacements along the critical slip surface, the framework provides a comprehensive assessment of slope stability. Its integration of unsaturated soil mechanics through the soil–water characteristic curve (SWCC) enables accurate modeling of soil behavior under varying conditions, which is crucial for slopes in semiarid or arid regions. The use of particle swarm optimization to identify critical slip surfaces and minimum FSG values ensures efficient and reliable optimization for slope design. Additionally, insights into the effects of SWCC fitting parameters aid in understanding and mitigating displacement risks, making the framework a robust tool for safer and more resilient slope designs.